In Afivo, the computational domain is defined by the coarse grid.

Step 1: calling a2_init()

First a user has to call m_a2_core::a2_init(), for example as shown below.

integer    :: n_cell   = 4      ! Boxes contain n_cell^dim cells
real(dp)   :: dr       = 1.0_dp ! Coarse grid spacing
integer    :: n_var_cc = 1      ! Number of cell-centered variables
integer    :: n_var_fc = 0      ! Number of face-centered variables
type(a2_t) :: tree             ! Will contain the quad/octree grid
call a2_init(tree, n_cell, n_var_cc, n_var_fc, dr)

The coarse boxes on this quadtree contain \(4 \times 4\) cells, and these cells have spacing of dr = 1.0.

Step 2: Setting the box spatial indices

The user can now choose how many boxes to add to the computational domain. For each box, a spatial index has to be given, which will determine where the box is located. The lowest index a box can have is [1, 1]. A box with index [2, 1] lies to the right (+x direction) of the box at [1, 1], etc. One could for example do the following:

integer, parameter  :: n_boxes = 2
integer             :: ix_list(2, n_boxes)
! Two boxes along x-direction
ix_list(:, 1) = [1, 1]        ! Box 1 at [1, 1]
ix_list(:, 2) = [2, 1]        ! box 2 at [2, 1]

The coordinates of these boxes would then be

box	x,y min	x,y max
1	0, 0	4, 4
2	4, 0	8, 4

To specify two boxes that touch in the y-direction, one would similarly do:

! Two boxes along y-direction
ix_list(:, 1) = [1, 1]        ! Box 1 at [1, 1]
ix_list(:, 2) = [1, 2]        ! box 2 at [1, 2]

Step 3: Optionally setting the neighbor information

Now the user can call m_a2_core::a2_set_base to create the computational domain:

call a2_set_base(tree, n_boxes, ix_list)

Afivo will automatically resolve the connectivity between neighbors. This routine accepts an optional argument with the connectivity, which can for example be used to specify periodic boundary conditions. An example is shown below:

integer :: nb_list(a$d_num_neighbors, n_boxes)
nb_list(:, :) = af_no_box      ! Start with default value
nb_list(a2_neighb_lowx, 1) = 2 ! Box 1's lower x-neighbor is box 2
nb_list(a2_neighb_lowy, 1) = 1 ! Box 1 is periodic in y-direction
nb_list(a2_neighb_lowy, 2) = 2 ! Box 2 is periodic in y-direction
call a2_set_base(tree, n_boxes, ix_list, nb_list)

By specifying the default value af_no_box, Afivo will automatically handle the internal connectivity between the boxes. Note also that the periodic boundary only needs to be specified from one side, the other sides are handled automatically.

Step 1: calling a2_init()

Step 2: Setting the box spatial indices

Step 3: Optionally setting the neighbor information

Examples